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What is Subject Content Knowledge in Mathematics?

On the Implications for Student Teachers’ Competence and

Confidence in Teaching Mathematics

Sheila HendersonBrian Hudson

University of Dundee

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Structure of presentation

• Prior work on student teachers’ competence and confidence in mathematics

• The nature of mathematics

• Current work and findings

• Ongoing project

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Raising Consciousness

(Luft and Ingham, 1955)

• Online Maths Assessment (OMA) created to address poor competences and confidence levels

• Johari profile– unconscious incompetence– conscious incompetence– unconscious competence– conscious competence

student’s own realisation prompts action

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Initial Results• Two thirds of BEd 1 students did not reach the 80%

recommended threshold in OMA and reported low levels of confidence

• Advanced qualification students less likely to reach threshold and 50% displayed low levels of confidence

• Subsequently all students reached threshold but engaged differently with OMA

• One third poor engagement

• Engagement and increased competence appears to lead to increased confidence

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On the contested (and distorted) nature ofmathematics

• Is it an abstract subject for an elite or should mathematics be for all?

• This (deductivist) style starts with a painstakingly stated list of axioms, lemmas and/or definitions. The axioms and definitions often look artificial and mystifyingly complicated. One is never told how these complications arose. The list of axioms and definitions is followed by carefully worded theorems. These are loaded with heavy-going conditions; it seems impossible that anyone should ever have guessed them. The theorem is followed by proof.

Lakatos (1976, p 142) • When this is presented in textbooks this product of human activity

"alienates itself" (ibid, p146) from the very human activity, which produced it.

• “dead geometry entombed in text books” (Geoff Giles, 1982)

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On the contested (and distorted) nature ofmathematics – in summary

Mathematical fundamentalism• Infallible and authoritarian• Dogmatic and absolutist

• Irrefutable and certain• Strict procedures• Rule following• Right and wrong answers• High stakes testing• Boring• De-motivating• Fear and anxiety• Alienation from the subject

itself

Mathematical fallibilism• Fallible and liberating• Critical thinking, growth &

change• Refutable and uncertain• Multiple solutions• Creative reasoning• Errors and mistakes• Evaluation & self assessment• Engaging• Motivating• Enjoyment and fulfilment• A creative human activity

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Current Findings

• Minority (25-30%) who continue to hold more fundamentalist beliefs

• Many students sit on the fence in stating their beliefs– confidence issue?

• Students had their own say

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Student Voices• … my low confidence in maths was down to teachers in my

standard grade year who weren't helpful, encouraging or positive in their teaching.

• I have always been scared of doing mental maths and did not enjoy maths at school …

• I recall the attitude of my class teacher in primary school … if you answered a mathematical question incorrectly your were belittled in front of your class mates and made to feel very inadequate.

• Fear of maths is a learned state which is the result of poor teaching.

• I have always believed that the wrong mode of teaching maths can have an extremely negative impact on the perception of maths for the learner.

• I have always enjoyed maths. I had a great maths teacher throughout my time in secondary and this motivated me to learn more and achieve in maths.

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Developing Mathematical Thinking in the Primary Classroom

• Project funded by Scottish Government

• 3 teachers from local authorities

• 20 teachers to take part in CPD

• Pre and post survey to gauge changes in practice and beliefs

• Maths specialist in every primary school?

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Questions?s.henderson@dundee.ac.uk

b.hudson@dundee.ac.uk